Manny Ramirez was no stranger to the trade rumor circuit during his time in Boston, long before the team actually went ahead and shipped him to the Dodgers in 2008. The deal that would have sent him to the Rangers in exchange for Alex Rodriguez is perhaps the most well known Manny non-trade, but WEEI.com's Rob Bradford says the team also came very close to shipping Ramirez to the Mets following the 2004 season.
Manny was fresh off being named World Series MVP, but the idea behind trading him was to use the savings for then free agents J.D. Drew and Adrian Beltre. Drew went on the sign with the Dodgers, Beltre the Mariners, though both found their way to Boston eventually.
There were several variations of the deal with the Mets, but the two constants were hotshot prospect Lastings Milledge and the veteran Cliff Floyd. At various other times, the package of players included Heath Bell and Ian Bladergroen, who the Mets eventually traded the the Red Sox for Doug Mientkiewicz.
The deal fell apart because of money. The Mets wanted to the Red Sox to kick in some of the $77MM left on Manny's deal, but Boston "wanted to get money back in the deal to pursue the available free agents." Bradford goes through some what-could-have-been scenarios in his article.
Ramirez went on to hit another 120 home runs and win another World Championship with the Red Sox, while the Mets fell just a game short of qualifying for the 2006 Fall Classic. They did, however, land one superstar responsible for helping the Red Sox end their World Series drought that offseason, signing Pedro Martinez to a four year, $53MM deal in December of 2004.